Integrated optical modulators have important applications in telecommunications and data-communications, as well as sensing. Optical intensity modulators generally facilitate imparting information onto laser light by modulating the intensity of an incident narrow-line (usually continuous-wave) laser signal. Relevant performance metrics for such modulators include modulation speed, sensitivity to the modulation drive signal and energy efficiency, extinction ratio (i.e., the ratio of the minimum to the maximum light intensity during a modulation cycle), and footprint. Resonant-cavity-based optical modulators (e.g., microcavity or microring modulators) typically enhance sensitivity by allowing light to circulate the cavity, and pass through a region of modulated index, many times on resonance. Further, their typically small footprint reduces drive capacitance. Both effects contribute to greater energy efficiency. However, conventional resonant modulators are subject to a well-known trade-off between sensitivity and modulation speed.
FIG. 1 illustrates an exemplary conventional resonant modulator 100, including a microring resonator 102 optically coupled to an optical waveguide 104. In operation, light enters the modulator at an input port 106 of the waveguide, and modulated light exits the modulator at a through port 108 of the waveguide. The modulator is characterized by a resonance frequency ω0 and a cavity loss rate rl of the microring, and an input coupling rate ri. Each of these quantities may be variable in response to a modulation drive signal and thus provide a modulation mechanism. When the resonance frequency ω0 or loss rl rate is modulated, the maximum modulation speed equals the optical resonance bandwidth (i.e., line width of the resonance), rendering a high optical resonance bandwidth desirable. On the other hand, sensitivity increases are achieved with bandwidth decreases because a narrower bandwidth requires a smaller resonance frequency shift to modulate the transmitted signal from the resonant peak to a high extinction point, and thus enables lower-energy switching between modulation states. The resulting trade-off between sensitivity and speed is therefore often summarized as a bandwidth-sensitivity product.
The relation between bandwidth and modulation speed results from the cavity dynamics during modulation. For example, when the resonance frequency ω0 is modulated, such modulation alternates the system between a state where the signal is on-resonance and a state where the signal is off-resonance. In a critically coupled resonator (i.e., for ri=rl), the transmission to the through port 108 is zero (corresponding, e.g., to a zero bit) on-resonance, but high (corresponding, e.g., to a one bit) off-resonance. On-resonance, the cavity (e.g., the interior of the microring) is loaded according to the finesse, inversely proportional to the line width, while off-resonance, the cavity is empty. Therefore, an instantaneous change in the resonance frequency causes a transition of the system from an old to a new steady-state photon population (optical energy) over a time interval of the cavity lifetime of a cavity photon. As a result, the through-port signal changes with a time constant of the cavity lifetime, which is the inverse of the cavity bandwidth.
When the resonance frequency is kept constant and the loss rate rl is instead modulated between rl=0 and rl=ri the system alternates between an all-pass state (one bit) and a critically coupled state (zero bit). The steady-state photon population of (optical energy in) the all-pass state is half that of the critically coupled state. Therefore, modulation again results in a transient state with a time-constant of the cavity lifetime. Practically, this limitation means that if the optical bandwidth is narrowed below the modulation bandwidth (e.g., the bandwidth of an electrical drive signal) to enhance modulation efficiency, the optical response to the modulation is slowed down relative to the drive signal. Modulation of the resonance frequency ω0 or loss rate rl thus results in a low-pass modulation response.
The bandwidth-sensitivity limit can at least partially be overcome by modulating the input coupling rate ri, rather the resonance frequency or loss rate. When the input coupling is modulated, the change in the through-port signal has two contributions: first, the input coupling determines directly and instantaneously the fraction of the cavity mode that is coupled out to the waveguide 104, and, second, the input coupling affects the photon lifetime, which, in turn, determines the cavity transients. In this case, the modulation frequency can exceed the optical bandwidth because a loaded cavity provides a source of light that can be instantaneously coupled out, with fast modulation unattenuated. However, low-frequency modulation is attenuated as a consequence of cavity dynamics. While the cavity population remains approximately in steady state during high-frequency modulation, low-frequency modulation results in cavity loading or depletion, causing variations in the signal strength of the all-pass signal. Thus, using input coupling rate modulation induces distortions of the modulated output signal at lower modulation frequencies.
Accordingly, there is a need for improved optical modulators that simultaneously achieve high modulation speed, high sensitivity, and high fidelity of the output signal.